Numerical Solutions Control by Entropy Analysis

The rate of entropy generation is used to estimate the average error of approximate numerical solutions of conductive and convective heat transfer problems with respect to the corresponding exact solutions. This is possible because the entropy analysis of simple problems, which have exact analytical solutions, shows that the rate of entropy generation behaves similarly to the average error of approximate solutions. Two test cases (transient two-dimensional heat conduction with Dirichlet boundary conditions and free convection between two plates at different temperatures with internal heat source) are discussed. Results suggest to use entropy analysis as a tool for the assessment of solution methods and to estimate the error of numerical solutions of thermal-fluid-dynamics problems.